1888-89.] Dr R. W. Felkin on Tropical Diseases. 
315 
Plate IX. 
Chart showing the geographical distribution of Elephantiasis arabum 
(Barbadoes leg). 
Plate X. 
Chart showing the distribution of Guinea-worm. 
Plate XI. 
Chart showing the geographical distribution of the Filaria sanguinis hominis, 
so far as at present known. 
Plate XII. 
Chart showing the occurrence of scurvy on land, as also the seas in which 
it is still sometimes met with in badly-found sailing ships. 
Plate XIII. 
Chart showing the distribution of tropical abscess of the liver. The regions 
in which it is most prevalent are indicated by a darker shade. 
Plate X1Y. 
Chart of the world illustrating the mean annual temperature of the 
tropical and sub-tropical zones. 
Plate XY. 
Chart showing the mean annual rainfall throughout the world. 
Plate XYI. 
Chart showing — A, the isoclinal lines with reference to pandemic waves of 
disease ; B, the prevailing winds on the ocean. 
Quaternion Note on a Geometrical Problem. 
By Professor Tait. 
(Read June 4, 1889.) 
The problem referred to is that of inscribing in a sphere a closed 
w-sided polygon, whose sides shall pass respectively through n given 
points which are not on the surface. Hamilton evidently regarded 
his solution of this question as a very tough piece of mathematics 
(see his Life , vol. iii. pp. 88, 426). In preparing a new edition of 
my Quaternions, I was led to a mode of treating this question which 
enables us to dispense with the brilliant feats of analysis which 
seem to be required in Hamilton’s method. 
The quaternions which Hamilton employed were such as change 
the radius to one corner of the polygon into that to the next by a 
